Chance Theory Research Articles

MEDIA PEMBELAJARAN SEBAGAI SARANA KOMUNIKASI MATEMATIKA DI SEKOLAH DASAR

R apid developments in information technology and communication today is based on the development of mathematics in the field of number theory, algebra, analysis, theory of chances and discrete mathematics. To master the technology and creating future required a strong mastery of mathematics from an early age. Standard mathematical competence and basic competence in elementary school (SD), Junior Secondary School (SMP) and High School (SMA) have been prepared with the intention to develop the ability to use mathematics in solving problems and communicating the idea or the idea of using symbols, tables, diagrams , and other media . At the elementary school where children are in the concrete operational stage and how to effectively communicate the idea of mathematical ideas is to use instructional media . T his paper will try to review the instructional media as one means of communication of mathematics learning in elementary school (SD). Kata kunci : komunikasi, media pembelajaran

Shortest path problem of uncertain random network

The shortest path problem is one of the most fundamental problems in network optimization. This paper is concerned with shortest path problems in non-deterministic environment, in which some arcs have stochastic lengths and meanwhile some have uncertain lengths. In order to deal with path problems in such network, this paper introduces the chance theory and uses uncertain random variable to describe non-deterministic lengths, based on which two types of shortest path in uncertain random networks are defined. To obtain the shortest paths, an algorithm derived from the Dijkstra Algorithm is proposed. Finally, numerical examples are given to illustrate the effectiveness of the algorithms.

A mathematical model of fluctuation noise based on the wavelet transform

A new model of white noise based on the wavelet transform has been proposed. This model is more adequate for solving some radiophysical tasks, such as the problem of electromagnetic waves reflecting from the ionosphere. Moreover, it was shown that in terms of probabilistic description of the random-process trajectories, the wavelet implementation of this random process is more likely (using the probability density functional offered by Amiantov). The wavelet properties and the famous theorems of mathematical analysis and theory of chances were used to develop our model: the mean value theorem and Lyapunov's central limit theorem. Our study resulted in obtaining a theorem on random-process expansion in terms of wavelet basis. It was also shown that the obtained results were in agreement with those of Kotelnikov.

Reliability analysis in uncertain random system

Reliability analysis of a system based on probability theory has been widely studied and used. Nevertheless, it sometimes meets with one problem that the components of a system may have only few or even no samples, so that we cannot estimate their probability distributions via statistics. Then reliability analysis of a system based on uncertainty theory has been proposed. However, in a general system, some components of the system may have enough samples while some others may have no samples, so the reliability of the system cannot be analyzed simply based on probability theory or uncertainty theory. In order to deal with this type systems, this paper proposes a method of reliability analysis based on chance theory which is a generalization of both probability theory and uncertainty theory. In order to illustrate the method, some common systems are considered such as series system, parallel system, k-out-of-n system and bridge system.

Ab alio movetur: Aristotle and Causal Determinism

AbstractThis paper addresses the contentious issue of Aristotle’s commitment to causal determinism, particularly as concerns the efficient cause. After distinguishing between determinism, fatalism, and necessitarianism, several common arguments in favor of indeterminist interpretations of Aristotle are examined and rebutted. Afterwards, several positive arguments in favor of a determinist interpretation are advanced. The paper then turns to Aristotle’s seminal theory of chance and his resistance to systemic/metaphysical conceptions of determinism. Finally the paper asks whether Aristotle’s theory of chance succeeds in vanquishing determinism, or even necessitarianism.

The Aristotelian Theory of Chance and its Application in Gersonides’ Biblical Exegesis

One of Gersonides’ fundamental postulates in his biblical exegesis is the idea, developed by the Maimonidean school, that Scripture teaches Aristotelian doctrines related to physics, metaphysics, and anthropology. For Gersonides, this applies chiefly to what he learned from Averroes’ commentaries on Aristotle, supplemented by other theories he developed on his own in the Wars of the Lord. In a recent article I showed that Gersonides uses the Aristotelian theory of chance as a research tool that allows him to reach conclusions about the issues he investigated in his own philosophical and theological work, the Wars of the Lord. Here I want to show that in four places in his Bible commentaries, Gersonides ascribed to biblical characters the use of the Aristotelian concept of chance as a demonstrative tool, just as he used it in the Wars of the Lord. These are: the authentication of Moses’ prophetic mission at the burning bush (Exod. 4:1–9); the Earth’s swallowing up of Korah and his company and of Dathan and Abiram (Num. 16:28ff.); Eliphaz’s speech in Job 4–5; and the survival of those who adhered to the Lord and did not worship Baal Peor when the Israelites were at Shittim (Deut. 4:4).

Chance and Regularities

The relationship between regularity and chance, or necessity and contingency, is a common concern of classical pragmatists. The metaphysical quality of this issue flows into the construction of postmodern discourse, although in a very different framework and, paradoxically, under the auspices of the anti-metaphysics that such a discourse claims. This paper proposes at first a brief reconstruction of the chance and regularity issue in postmodernism; then Peirce’s cosmological-metaphysical theory of chance, namely his ‘tychism,’ is recalled as a fruitful suggestion to avoid the conceptual split between chance and regularity. Subsequently, considering the family resemblances between postmodernism and Rorty’s neo-pragmatism, the insistence upon history and contingency that stands out in his work will be tackled as a ‘postmodern tychism’ that, in fact, does not fit too-easy readings according to which he would have turned pragmatism into an extreme form of irrationalism and radical moral relativism. In particular, this paper aims to enlighten Rorty’s effort to re-propose, with new and more refined philosophical tools, the great challenge posed by the classical pragmatists: namely, the challenge to translate the pathos of contingency into an anti-dogmatic ethos, that is a cultural stance that might be able to combine the rejection of absolutes with the commitment to construct meanings and values hosting argumentative interpersonal and intercultural practices as the ‘rule’ of our moral history.

Chance Single Sampling Plan for Variables

This paper considers the design of single sampling plan for variables when the experimental values are treated as observations on independently and identically distributed normal random variables with fuzzy mean value. The design makes use of Liu's (2008) model IV of Chance Theory. Sampling Plans determined by the sample sizes and acceptance numbers are constructed for situations involving imprecise parameter on using chance theory. The process of determining sample sizes and acceptance threshold values has been carried out on assuming the observed values have hybrid normal distribution. Optimal chance sampling plans for variables are also determined by using minimum angle criterion for different choices of fuzzy risks.

A perda da chance na jurisprudência do Superior Tribunal de Justiça – os (des)caminhos de uma compreensão teórica

The article aims at demonstrating that, with the modification of the concept of wrongful damage in order to embrace not only the violation of subjective rights but also the injury caused to legitimate interests, the recognition of a new damage category, called the loss of chance, became possible. From this assumption, based on national and foreign doctrines (mainly French and Italian), it analyses the Brazilian Superior Court of Justice’s decisions concerning this issue that were the result of a search realized by the words “loss” and “chance”. For the purposes of the study, all decisions that the central problem was not directly concerned to the theory of loss of chance or it were related to medical liability have been eliminated from the sample. Because of that, the analysis is restricted to the decisions in which the classical loss of chance theory has been applied, meaning the cases in which there is a frustration of an aleatory process at the end of which there would be an advantage or the possibility to avoid a loss, but noboby will ever be capable of knowing the final result. This approach highlights, thus, how has been the theory acceptation in the Brazilian Superior Court of Justice and punctuates the successes and misconceptions of the comprehension and characterization of this new type of damage. Furthermore, it also demonstrates there is no concurrency in the Superior Court of Justice, whose decisions sometimes do not admit the compensation for the loss of chance; every now and then, although they recognize the loss of chance as a new type of damage, they characterize it as consequential damages or lost profits or, instead, only as aggregating the value of moral damage.

An Uncertain Random Programming Model for Project Scheduling Problem

Project scheduling problem PSP is to determine the resource allocation schedule for the trade-off between the project cost and the completion time. In this paper, PSP in the environment with uncertainty and randomness simultaneously is considered. In detail, the concepts of uncertain variable and uncertain random variable are introduced. Based on some concepts and theorems of chance theory, an uncertain random project scheduling model is built. For some special case, the proposed uncertain random programming model is transformed to a crisp mathematical programming model. Besides, uncertain random simulation techniques and genetic algorithm are integrated into a hybrid intelligent algorithm for searching the quasi-optimal schedule.

Some Concepts and Theorems of Uncertain Random Process

To deal with a system with both randomness and uncertainty, chance theory has been built and an uncertain random variable has been proposed as a generalization of random variable and uncertain variable. Correspondingly, as a generalization of both the stochastic process and the uncertain process, this paper will propose an uncertain random process. In addition, some special types of uncertain random processes such as stationary increment process and renewal process will also be discussed.

Construction and Initial Validation of the Planned Happenstance Career Inventory

This study was conducted to develop and initially evaluate the psychometric properties of the Planned Happenstance Career Inventory (PHCI), which aims to assess skill in using chance events to develop career opportunities. After item generation and exploratory factor analysis, 130 original items were reduced to 25 items across 5 factors (5 items for each corresponding factor). Multigroup confirmatory factor analysis confirmed the validity of this 5‐factor structure, and the goodness of fit showed an adequate fit to the observed data for both women and men. Results showed that PHCI subscales correlated moderately and in expected directions with career preparation, career decision‐making self‐efficacy, and career stress. These findings suggest that the PHCI, which assesses 5 dimensions of career‐related planned happenstance skill, shows promise as a useful tool for facilitating understanding of the influence of chance events on career choice behavior.

A short history of probability theory and its applications

It is remarkable that a science (Probability) which began with consideration of games of chance, should have become the most important object of human knowledge.Probability has reference partly to our ignorance, partly to our knowledge. … The Theory of chances consists in reducing all events of the same kind to a certain number of cases equally possible, that is, such that we are equally undecided as to their existence; and determining the number of these cases which are favourable to the event sought. The ratio of that number to the number of all the possible cases is the measure of the probability . …P.S. LaplaceThe true logic of this world is to be found in theory of probability.James Clark MaxwellThis paper deals with a brief history of probability theory and its applications to Jacob Bernoulli's famous law of large numbers and theory of errors in observations or measurements. Included are the major contributions of Jacob Bernoulli and Laplace. It is written to pay the tricentennial tribute to Jacob Bernoulli, since the year 2013 marks the tricentennial anniversary of Bernoulli's law of large numbers since its posthumous publication in 1713. Special attention is given to Bayes’ celebrated theorem and the famous controversy between the Bayesian and frequentism approaches to probability and statistics. This paper is also written to pay a special tribute to Thomas Bayes since the year 2013 marks the 250th anniversary of Bayes’ celebrated work in probability and statistics, since its posthumous publication in 1763. This is followed by a short review of the modern axiomatic theory of probability first created by A.N. Kolmogorov in 1933.

The Formation of Ratings as a Multidimensional Function. Express-Ratings and Time Ratings Based on the Bayes Theorem

It is suggested in the article to calculate express rating and time rating of the study objects according to the theory of chances – Bayes theorem. As a random event is used the achievement of certain level of reliability by the study object. It is proposed to estimate express rating as one-dimensional assessment of input data and time rating as multidimensional assessment of input data.

Chance distribution of the maximum flow of uncertain random network

A network is called uncertain random network if some arc capacities of the network are uncertain variables and others are random variables. The main purpose of this paper is to study the maximum flow in an uncertain random network. Under the framework of chance theory, this paper obtains chance distribution of the maximum flow of an uncertain random network. At the same time, the expected value of maximum flow is given for an uncertain random network. A new method is derived to calculate chance distribution of the maximum flow for an uncertain random network.

Subadditivity of chance measure

Chance theory is a mathematical methodology for dealing with indeterminacy phenomena involving uncertainty and randomness. In this paper, some properties of chance space are investigated. Based on this, the subadditivity theorem, null-additivity theorem, and asymptotic theorem of chance measure are proved.

Some formulas of variance of uncertain random variable

Uncertainty and randomness are two basic types of indeterminacy. Chance theory was founded for modeling complex systems with not only uncertainty but also randomness. As a mixture of randomness and uncertainty, an uncertain random variable is a measurable function on the chance space. It is usually used to deal with measurable functions of uncertain variables and random variables. There are some important characteristics about uncertain random variables. The expected value is the average value of uncertain random variable in the sense of chance measure and represents the size of uncertain random variable. The variance of uncertain random variable provides a degree of the spread of the distribution around its expected value. In order to describe the variance of uncertain random variable, this paper provides some formulas to calculate the variance of uncertain random variables through chance distribution and inverse chance distribution. Several practical examples are also provided to calculate the variance for through chance distribution inverse chance distribution.

Theory of Chances: Novel Stochastic Chains: Linear Algebraic Approach

In this research paper, the author proposes the idea of allowing the chance (like probability) to assume negative and complex values. Novel stochastic chains based on real/complex valued 2p L chances are formally discussed. Also, the theory of 1 L chances is discussed. Chance number theory is briefly discussed.

Project Scheduling Problem with Uncertain Variables

Project scheduling problem is mainly to determine the schedule of allocating resources in order to balance the total cost and the completion time. This paper chiefly uses chance theory to introduce project scheduling problem with uncertain variables. First, two types of single-objective programming models with uncertain variables as uncertain chance-constrained model and uncertain maximization chance-constrained model are established to meet different management requirements, then they are extended to multi-objective programming model with uncertain variables.

The Best Humean System for Statistical Mechanics

Classical statistical mechanics posits probabilities for various events to occur, and these probabilities seem to be objective chances. This does not seem to sit well with the fact that the theory’s time evolution is deterministic. We argue that the tension between the two is only apparent. We present a theory of Humean objective chance and show that chances thus understood are compatible with underlying determinism and provide an interpretation of the probabilities we find in Boltzmannian statistical mechanics.